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A new family of locally correctable codes based on degree-lifted algebraic geometry codes
2013
Proceedings of the 45th annual ACM symposium on Symposium on theory of computing - STOC '13
We describe new constructions of error correcting codes, obtained by "degree-lifting" a short algebraic geometry base-code of block-length q to a lifted-code of block-length q m , for arbitrary integer m. The construction generalizes the way degree-d, univariate polynomials evaluated over the q-element field (also known as Reed-Solomon codes) are "lifted" to degree-d, m-variate polynomials (Reed-Muller codes). A number of properties are established: Rate The rate of the degree-lifted code is
doi:10.1145/2488608.2488714
dblp:conf/stoc/Ben-SassonGKKS13
fatcat:hwixwvv265aypdsm6qrmbfwnwq